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Triangular NURBS and their dynamic generalizations

1997
*
Computer Aided Geometric Design
*

*Triangular*

*B*-

*splines*are a new tool for modeling a broad class

*of*objects defined

*over*

*arbitrary*, nonrectangular domains. ... They provide

*an*elegant and unified representation scheme for all piecewise continuous polynomial

*surfaces*

*over*planar

*triangulations*. ... Acknowledgments We would like to thank Professor Hans-Peter Seidel

*of*Universit~it Erlangen for kindly making available the software for

*triangular*

*B*-

*spline*

*surfaces*that he developed with Mr. ...

##
###
Dynamic manipulation of triangular B-splines

1995
*
Proceedings of the third ACM symposium on Solid modeling and applications - SMA '95
*

As

doi:10.1145/218013.218084
dblp:conf/sma/QinT95
fatcat:aadkvyhr7rf2zhnzruekddjqny
*an*alternative, we develop a new model based on the elegant*triangular**B*-*spline*geometry and principles*of*physical dynamics. ... They are useful for modeling a broad class*of*complex objects defined*over**arbitrary*, nonrectangular domains. ... Acknowledgments We are grateful to Professor Hans-Peter Seidel for kindly making available the software for*triangular**B*-*spline**surfaces*that he developed with Philip Fong. ...##
###
Page 6644 of Mathematical Reviews Vol. , Issue 94k
[page]

1994
*
Mathematical Reviews
*

Franz Peherstorfer (A-LINZ; Linz)
94k:65017 65D07 41A15
Fong, Philip (3-WTRL-C; Waterloo, ON);
Seidel, Hans-Peter (D-ERL-GD; Erlangen)

*An**implementation**of**triangular**B*-*spline**surfaces**over**arbitrary**triangulations*... Fong “Shape control for*B*-*splines**over**arbitrary**triangulations*”, Master’s Thesis, Univ. Waterloo, Waterloo, ON, 1992; per bibl.]. 65 NUMERICAL ANALYSIS 6644 Given*an**arbitrary**triangulation*T*of*R? ...##
###
Splines and geometric modeling
[chapter]

2004
*
Handbook of Discrete and Computational Geometry, Second Edition
*

The

doi:10.1201/9781420035315.ch53
fatcat:e7evq2b77ba5lj3vxlcxwxxzda
*surface*scheme is*an*approximation scheme based on blending functions and control points and allows the modeling*of*C k,1 continuous piecewise polynomial*surfaces**of*degree k*over**arbitrary**triangulations*...*Splines**over**arbitrary**triangulations**of*the parameter plane were rst considered by Dahmen and Michelli DM82 and H ollig Hol82 . ...##
###
A C 1 Globally Interpolatory Spline of Arbitrary Topology
[chapter]

2005
*
Lecture Notes in Computer Science
*

Starting from the Powell-Sabin

doi:10.1007/11567646_25
fatcat:vbzdt43br5c7zcyeglnidihaly
*spline*as a building block, we integrate the concepts*of*global parametrization, affine atlas, and*splines*defined*over*local, open domains to arrive at*an*elegant, easy-to-use ... The proposed global*spline*scheme enables the rapid*surface*reconstruction and facilitates the shape editing and analysis functionality. ... Figure 3 illustrates*an*example*of*Powell-Sabin*spline**surface**over*a planar*triangulated*domain. Note that, their basis functions*B*j i (u) vanish outside the molecule M i (see Figure 3 (e-h)). ...##
###
Spline Thin-Shell Simulation of Manifold Surfaces
[chapter]

2006
*
Lecture Notes in Computer Science
*

The deformation is represented as a linear combination

doi:10.1007/11784203_53
fatcat:odauljhibzfi5g7qxgvi6m6qxy
*of**triangular**B*-*splines**over*shell*surfaces*, then the dynamics*of*thin-shell simulation is computed through the minimization*of*Kirchhoff-Love energy ... In particular, we systematically extend the*triangular**B*-*spline*FEM from planar domains to manifold domains. ... For examples, manifold*triangular**B*-*splines*are piecewise polynomial defined on the manifold domain*of**arbitrary**triangulation*. ...##
###
Incorporating Rigid Structures in Non-rigid Registration Using Triangular B-Splines
[chapter]

2005
*
Lecture Notes in Computer Science
*

features (C 0 continuity) along the interface between deformable regions and rigid structures, because

doi:10.1007/11567646_20
fatcat:lbcoo4ezbzeilcft567zjzgb7i
*of*the unique advantages offered by*triangular**B*-*splines*, such as flexible*triangular*domain, local ... In this paper, we introduce a novel registration technique that models local rigidity*of*pre-identified rigid structures as well as global non-rigidity in the transformation field using*triangular**B*-*splines*... Pfeifle and Seidel [19] presented*an*efficient algorithm to evaluate quadratic*triangular**B*-*splines*and Franssen et al. [20] extended it to*triangular**B*-*splines**of**arbitrary*degree. ...##
###
Multilevel refinable triangular PSP-splines (Tri-PSPS)

2015
*
Computers and Mathematics with Applications
*

*of*the PSPS can be directly built from

*an*

*arbitrary*set

*of*polygons that partitions a giving parametric domain. ... Secondly, Tri-PSPS are

*an*additive

*triangular*

*spline*technique, where the

*spline*function built from a given triangle can be replaced with a set

*of*refined

*spline*functions built on a set

*of*smaller triangles ... The function built in this way for

*an*

*arbitrary*polygon is independent

*of*the ways that the given polygon is

*triangulated*. ...

##
###
Surface reconstruction using bivariate simplex splines on Delaunay configurations

2009
*
Computers & graphics
*

Unlike existing

doi:10.1016/j.cag.2009.03.013
fatcat:erkdsfmsn5d6zcygwex4mcy6lm
*surface*reconstruction methods based on*triangular**B*-*splines*(or DMS*splines*), in which auxiliary knots must be explicitly added in advance to form a knot sequence for construction*of*each ... In this paper, we develop a novel shape modeling framework to reconstruct a closed*surface**of**arbitrary*topology based on this new*spline*scheme. ... This work is partially supported by NSF IIS-0710819, NSF IIS-0326338, Louisiana Board*of*Regents PFund: NSF(2009)-PFUND-133, and the Natural Science Foundation*of*China 60773179. ...##
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Construction of multiresolution triangular B-spline surfaces using hexagonal filters

2000
*
The Visual Computer
*

We present multiresolution

doi:10.1007/s003710000073
fatcat:iecsy2xskvhxjdvgvlsmr7rrjy
*B*-*spline**surfaces**of**arbitrary*order defined*over**triangular*domains. ... The scheme works for*splines**of*any order where the fundamental building blocks*of*the*surface*are hierarchies*of**triangular**B*-*spline*scaling functions and wavelets spanning the complement spaces between ...*triangular**B*-*spline**surfaces**of**arbitrary*polynomial order. ...##
###
Manifold splines

2005
*
Proceedings of the 2005 ACM symposium on Solid and physical modeling - SPM '05
*

We choose

doi:10.1145/1060244.1060249
dblp:conf/sma/GuHQ05
fatcat:inyekbp2gvf3tlerj6qoiv236i
*triangular**B*-*splines*mainly because*of*its generality and many*of*its attractive properties. ... Based on our theoretical breakthrough, we also develop a set*of*practical algorithms to generalize*triangular**B*-*spline**surfaces*from planar domains to manifold domains. ...*over**arbitrary*planar*triangulations*, and they generalize tensor-product*B*-*splines*. ...##
###
Manifold splines

2006
*
Graphical Models
*

We choose

doi:10.1016/j.gmod.2006.03.004
fatcat:vlkc4cify5ffjf7dflyxy36cwa
*triangular**B*-*splines*mainly because*of*its generality and many*of*its attractive properties. ... Based on our theoretical breakthrough, we also develop a set*of*practical algorithms to generalize*triangular**B*-*spline**surfaces*from planar domains to manifold domains. ...*over**arbitrary*planar*triangulations*, and they generalize tensor-product*B*-*splines*. ...##
###
Fitting Surface of Free Form Objects using Optimized NURBS Patches Network with Evolutionary Strategies (mu + lambda) - ES

2007
*
Procedings of the British Machine Vision Conference 2007
*

We propose

doi:10.5244/c.21.99
dblp:conf/bmvc/BranchPB07
fatcat:nxb4irsoabainbo2jfrz6v22mm
*an*algorithm to produce a 3-D CAD model from a set*of*range data, based on non-uniform rational*B*-*splines*(NURBS)*surface*fitting technique. ... The quadrilateral obtained mesh is regularized by means*of*the use*of*geodesic curves and*B*-*splines*to obtain a new adequate grid on which to draw NURBS*surfaces*. ... The formulation*of*C 1 continuity presented in this paper can be generalized, because it can be used to approximate regular and irregular neighborhoods which present model processes regardless*of*partitioning ...##
###
Supporting Automated Pen and Ink Style Surface Illustration with B-Spline Models

2011
*
Cartography and Geographic Information Science
*

In

doi:10.1559/15230406382161
fatcat:lnjrphw6czdzjpphc33h2qpc7m
*B*,*surface*masking resolves the intersection problem. Figure 7 . 7*An**arbitrary*grid rendered as a*B*-*spline**surface*with non-emissive gray shading. ... Figure 7 shows*an*example*of*a rendered*B*-*spline**surface*shaded with a non-emissive color. ...##
###
Efficient evaluation of triangular B-spline surfaces

2000
*
Computer Aided Geometric Design
*

Evaluation routines are essential for any application that uses

doi:10.1016/s0167-8396(00)00030-3
fatcat:lfhuzyv4cfd5xoyeqyfc3ktwwm
*triangular**B*-*splines*. This paper describes*an*algorithm to efficiently evaluate*triangular**B*-*splines*. ... The novelty*of*the algorithm is its generality: there is no restriction on the degree*of*the*B*-*spline*or on the dimension*of*the domain. ... Definition*of**triangular**B*-*splines*Definition 2.6 [*Triangular**B*-*splines*] A*triangular**B*-*splines*is a piecewise polynomial function defined*over**an**arbitrary*polygonal domain in rn? ...
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